Subgroups — #23780936

Order 10404.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃⋊(C₁₇⋊D₁₇)	—	6	2	no	—
4	#11923884	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	#10597479	—	17	2	no	maximal
7	C₁₇⋊D₁₇	—	9	1	no	—
8	C₃⋊D₅₁	—	17	2	no	—
9	C₃⋊D₅₁	—	34	8	no	—
10	C₁₇²	#157	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₁₇	—	2	8	no	—
12	C₃²×C₁₇	#595	1	2	yes	complemented
13	D₅₁	—	102	32	no	—
14	D₅₁	—	102	4	no	—
15	#595	—	153	2	no	—
16	C₃×C₁₇	—	2	32	no	—
17	C₃×C₁₇	—	2	4	no	—
18	#157	—	289	1	no	Hall
19	D₁₇	—	306	8	no	—
20	D₁₇	—	153	2	no	—
21	C₃⋊D₃	—	289	1	no	—
22	C₁₇	—	2	8	no	—
23	C₁₇	#10597479	1	2	yes	complemented
24	C₃²	#11923884	1	1	yes	characteristic, complemented, Sylow
25	D₃	—	1734	2	no	—
26	C₄	—	2601	1	no	Sylow
27	C₃	—	2	2	no	—
28	C₂	—	2601	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇²	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂
LCS	G ▷ C₃²×C₁₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.